from __future__ import division
import unittest, csv, string, datetime
from numpy import floor, reshape, size, array, arange
from dateutil.relativedelta import relativedelta
import sys

def xirr(cash_flows, dates, yld=0.1, maxiter=50):
    """
    @param cash_flows list of cashflows
    @param dates list of datetime.date objects
    @param yld guess for rate of return
    @param maxiter maximum iterations
    """
    assert len(dates) == len(cash_flows)
    for date in dates:
        assert type(date) == datetime.date

    date_ordinals = array([x.toordinal() for x in dates])
    cash_flows = array(cash_flows)

    #number of years in cash flow FIXME: use max and min date, not first and last in list
    func = int(floor(yearfrac(dates[0], dates[-1])))
    if func == 0:
        func = 1
    #matlab: tf = func*(dates(:,loop)-dates(1,loop))/(datemnth(dates(1,loop),12*func,0,0)-dates(1,loop));
    tf = func*(date_ordinals - date_ordinals[0]) / (dates[0] + relativedelta(months = +12*func) - dates[0]).days

    # Determine the best guess for yld
    min_result = sys.maxint
    best_yld = None
    for yld in arange(-0.9, 1, 0.1):
        if yld == 0:
            continue
        result_f = abs(sum(cash_flows / ((1 + yld)**tf)))
        if result_f < min_result:
            min_result = result_f
            best_yld = yld

    yld = best_yld
    print "Using guess yld=", yld

    func = 2
    k = 1
    #Newton's Method
    while abs(func) > 1.e-6:
        #cash flow polynomial
        func = sum(cash_flows / ((1 + yld)**tf))
        #%(CF poly)'
        f_prime = -sum((cash_flows/((1 + yld)**tf)) * (tf/(1 +yld)))
        if f_prime == 0:
            yld = None
            break

        delta = -func/f_prime
        yld = yld + delta
        k += 1
        if k == maxiter + 1:
            print 'Number of maximum iterations reached.'
            print 'Please increase MAXITER or use different GUESS.'
            yld = None
            break
    return yld

def yearfrac(date1, date2):
    wYears = int(floor(abs((date1 - date2).days) / 365.))
    date1W = datetime.date(date1.year + wYears, date1.month, date1.day)
    numerator = (date1W - date2).days
    try:
        denominator = (date1W - datetime.date(date1W.year + 1, date1W.month, date1W.day)).days
    #-----handle weird leap year case
    except ValueError:
        date1W = date1W + datetime.timedelta(1)
        denominator = (date1W - datetime.date(date1W.year + 1, date1W.month, date1W.day)).days
    yearFraction = numerator / float(denominator)
    return yearFraction + wYears

-Carlos

I don’t understand the problem you described whereby “you’ve been investing for ten years but have built up the investment by adding to it each year, you could have the same average annualised return if the early years were excellent and the latter years poor, or vice versa.”

Maybe the XIRR function solves the problem you describe (I think it does).

XIRR

More on XIRR

Anyways, yes I’m doing this for fun.

I picked up a copy of Quicken 2006 for free (stuck on the front of a $6 investment magazine).

ps. Even Quicken doesn’t calculate annualised returns perfectly. It gets very messy when you are adding to or selling part of an existing position – you have to track individual lots. You also can’t just use arithmetic averaging of returns.

I think the easiest method to follow is to just pretend your portfolio is a big ‘black box’, and record all dollar amounts in and out and then iteratively calculate what annual rate of return applied to the model results in the same ending value as your real portfolio. However, unless you have kept a fairly constant amount invested over the total period, this figure is pretty meaningless. eg. If you’ve been investing for ten years but have built up the investment by adding to it each year, you could have the same average annualised return if the early years were excellent and the latter years poor, or vice versa. But althought the average annualised returns are the same the end result is different! To adjust for this you’d have to WEIGHT the return calculation based on the amount you had invested at any time… It all gets way too hard to be of use. You’re better off concentrating on saving more in the early years, and minimising transaction and management costs once you have a reasonable amount invested (say > 5x your annual salary).